probability assessment

Question

5.12. The tax situation for houses with rentals is a bit more complicated than

we presented in the chapter. On one hand, Sanjay and Sarah must pay

taxes on any rental income, which will increase their expenses. On the

other hand, Sanjay and Sarah can depreciate the percentage of the home

rented and can deduct a percentage of expenses for repair and upkeep.

For example, 35% of the Charlotte house is rented, thus the depreciation

Questions and Problems 227

amount (a straight-line depreciation over 27 years) for Charlotte is

Page 15%$7,778. In addition, 35% of the

repair and upkeep cost for Charlotte can be deducted from the rental

income before computing the taxes. Incorporating these additional lia-

hilities and deductions into net annual cost gives:

Net Annual Costs - Total Costs - (Rental Income + Tax Deduction).

Rental Income (Monthly Rent Months Occupied).

Tax Deduction = (Tax Ratex (1-Percentage Rented) Interest Paid)

+Depreciation

-(Tax Ratex (1-Percentage Rented) x P % x Mortgage)

Percentage Rented x Price

Total Costs Mortgage + Home Owner's Insurance

+ Repair & Upkeep + (House Price x Property Tax Rate)

+ Taxes on Rental Income

- Mortgage + Home Owner's Insurance + Repair & Upkeep

+ (House Price x Property Tax Rate) + Tax Rate

x (Monthly Rent x Montis Occupied)

- (Percentage Rented x Repair & Upkeep)

Using this more complete formula, we can compute the Net Annual Cost

of each property. Note that Sanjay and Sarah need only pay the taxes on

rental income when there is a renter, but they can deduct depreciation

whether the apartment is rented or not. Thus, depreciation provides

Sanjay and Sarah with a small buffer when the apartment is vacant.

a) Using the variables and the upper and lower bounds given in Table 5.2

run a one-way sensitivity analysis on Sanjay and Sarah's three housing

alternatives. Interpret the results.

b) How do the sensitivity results differ from what we found in the chapter?